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List of C++ software and tools
This is a list of notable software and programming tools for the C++ programming language, including libraries, web frameworks, programming language implementations, compilers, integrated development environments (IDEs), and other related software development utilities. == Compilers and IDEs == AMD Optimizing C/C++ Compiler — proprietary fork of LLVM + Clang for Linux C++Builder — rapid application development (RAD) environment Clang – compiler front end for C, C++, and Objective-C, part of LLVM CLion — C++ IDE by JetBrains Code::Blocks — open-source cross-platform IDE that supports multiple compilers including GCC, Clang and Visual C++ CodeLite — cross-platform IDE for the C/C++ programming languages using the wxWidgets toolkit CodeSynthesis XSD – XML Data Binding compiler Dev-C++ — MinGW or TDM-GCC 64bit port of the GCC as its compiler GCC – GNU Compiler Collection Intel C++ Compiler – proprietary high-performance compiler by Intel KDevelop — IDE part of the KDE project and is based on KDE Frameworks and Qt, the C/C++ backend uses Clang. Microsoft Visual C++ – proprietary C++ compiler and IDE for Windows Oracle Developer Studio — Solaris, OpenSolaris, RHEL, and Oracle Linux operating systems. Qt Creator — part of the SDK for the Qt GUI application development framework and uses the Qt API SlickEdit — text editor and IDE Turbo C++ – legacy C++ IDE and compiler popular in the 1990s Understand — IDE that enables static code analysis through an array of visuals, documentation, and metric tools. Visual Studio — integrated development environment by Microsoft that supports C++ Visual Studio Code — integrated development environment by Microsoft that supports C++ Xcode — Apple IDE to develop macOS, iOS, iPadOS, watchOS, tvOS, and visionOS that supports C++ source code. == Debuggers == Allinea DDT – a graphical debugger dbx — a proprietary source-level debugger GNU Debugger – portable debugger that runs on many Unix-like systems Modular Debugger — a C/C++ source level debugger for Solaris and derivates Undo LiveRecorder — time travel debugger == Libraries == Active Template Library – template-based C++ classes developed by Microsoft Apache MXNet — deep learning framework Apache Xerces – parsing, validating, and serializing and manipulating XML. Asio — networking and low-level I/O library Bitpit — scientific computing and mesh manipulation library Boost — collection of peer-reviewed libraries Botan — cryptography library C++ AMP – easy way to write programs that compile and execute on data-parallel hardware, such as graphics cards and GPUs C++ Standard Library — standard library for the language C++/WinRT — library for Microsoft's Windows Runtime platform, designed to provide access to modern Windows APIs. C3D Toolkit — geometric modeling kernel Caffe — deep learning framework CAPD — library for rigorous numerics and dynamical systems Cassowary — constraint-solving toolkit that efficiently solves systems of linear equalities and inequalities Cinder — library for creative coding ClanLib — cross-platform game SDK CMU Sphinx — speech recognition system Crypto++ — cryptographic algorithms library Dlib — general-purpose cross-platform library Dune — partial differential equations using grid-based methods fastText — text representation and text classification library FLTK — GUI toolkit Geospatial Data Abstraction Library — geospatial data access library GDCM — image library General Polygon Clipper — polygon clipping library GiNaC — computer algebra system that uses Class Library for Numbers for implementing arbitrary-precision arithmetic GLFW — OpenGL and window management library HarfBuzz — text rendering and typesetting library High Efficiency Image File Format — digital container format for storing individual digital images and image sequences ITK — image analysis library Integrated Performance Primitives — domain-specific functions that are highly optimized for diverse Intel architectures Jackets library — GPU computing library JSBSim — open-source flight dynamics model JUCE — framework for audio applications KDE Frameworks — collection of libraries from the KDE project KFRlib — digital signal processing framework LEMON — library for optimization and graph problems LevelDB — key–value database library Libdash — MPEG-DASH streaming library libLAS — reading and writing geospatial data encoded in the ASPRS laser (LAS) file format libsigc++ — typesafe callbacks LibRaw — free and open-source software library for reading raw files from digital cameras libSBML — application programming interface (API) for the SBML (Systems Biology Markup Language) LIBSVM — sequential minimal optimization (SMO) algorithm for kernelized support vector machines Libx — DirectX .X files graphics library Loki — collection of design patterns LIVE555 — multimedia streaming library Metakit — embedded database library Microsoft Cognitive Toolkit — deep learning toolkit Microsoft Foundation Class Library — object-oriented library for developing desktop applications for Windows Microsoft SEAL — homomorphic encryption library mlpack — machine learning and AI library Mobile Robot Programming Toolkit — robotics research library Object Windows Library — Object Windows Library, superseded by VCL Open Cascade — CAD and 3D modeling library Open Asset Import Library — 3D model import library to provide a common API for different 3D asset file formats OpenCV – computer vision and machine learning library OpenFOAM — computational fluid dynamics toolkit OpenH264 — real-time encoding and decoding video streams in the H.264/MPEG-4 AVC format OpenImageIO — image processing library Open Inventor — higher layer of programming for OpenGL OpenNN — neural networks library OpenVDB — sparse volume data library openFrameworks — creative coding toolkit OpenRTM-aist — robotics middleware library Oracle Template Library — database access that supports IBM Db2 and Open Database Connectivity Orfeo toolbox — remote sensing image processing library OR-Tools — operations research and optimization library Parallel Augmented Maps — ordered sets, ordered maps, and augmented maps. Parallel Patterns Library — Microsoft library that provides features for multicore programming PhysX — physics simulation engine POCO C++ Libraries — general-purpose libraries for software development Poppler — PDF rendering library Protocol Buffers — data serialization library Qt — cross-platform widget toolkit QuantLib — quantitative finance library RocksDB — key–value database library ROOT — data analysis framework from CERN ROS — robotics middleware Scintilla — source code editing component SDL – Simple DirectMedia Layer, cross-platform development library for multimedia applications SFML – Simple and Fast Multimedia Library Shark – open-source machine learning library Shogun — machine learning toolbox Skia — 2D graphics library Snappy — compression library Sound Object Library — music and audio development Standard Template Library — library of containers and algorithms Stapl — parallel computing library SymbolicC++ — symbolic computation library TerraLib — GIS library Tesseract OCR — optical character recognition engine Threading Building Blocks — parallel computing library ThreadWeaver — concurrency framework Tiny-dnn — lightweight deep learning library TinyXML — lightweight XML parser Tkrzw — key–value databases VTD-XML — XML processing library wxWidgets — cross-platform GUI toolkit x265 — video encoding library for HEVC XGBoost — gradient boosting library Windows Template Library — Win32 development === Mathematical and numerical libraries === == Tools == Akonadi — a C++/Qt framework and storage service for personal information management BALL – framework and set of algorithms and data structures for molecular modelling and computational structural bioinformatics Boehm garbage collector – conservative garbage collector CEGUI — C++ GUI library ClanLib – video game SDK CMake — cross-platform build system for C++ projects Confidential Consortium Framework – blockchain infrastructure framework DaviX – WebDAV client Doxygen — documentation generator for C++ and other languages FLTK — Fast Light Toolkit, cross-platform GUI library Fox toolkit — C++ GUI toolkit GDB — GNU Project debugger, often used with C and C++ gtkmm — official C++ interface for the popular GUI library GTK HOOPS Visualize — 3D computer graphics HPX — partitioned global address space Parallel programming Runtime System JUCE — cross-platform C++ audio and GUI framework LessTif — free clone of Motif GUI toolkit MFC — Microsoft Foundation Class library Nana — modern C++ GUI toolkit PTK Toolkit — 2D rendering engine and SDK, and portability options. Qt — cross-platform C++ GUI toolkit Rogue Wave — C++ GUI toolkit TnFOX — C++ GUI toolkit Ultimate++ — cross-platform C++ GUI framework Valgrind — tool suite for debugging and profiling C/C++ programs wxWidgets — cross-platform C++ GUI toolkit x265 — encoder for creating digital video streams in the High Efficiency Vid
Inauthentic text
An inauthentic text is a computer-generated expository document meant to appear as genuine, but which is actually meaningless. Frequently they are created in order to be intermixed with genuine documents and thus manipulate the results of search engines, as with Spam blogs. They are also carried along in email in order to fool spam filters by giving the spam the superficial characteristics of legitimate text. Sometimes nonsensical documents are created with computer assistance for humorous effect, as with Dissociated press or Flarf poetry. They have also been used to challenge the veracity of a publication—MIT students submitted papers generated by a computer program called SCIgen to a conference, where they were initially accepted. This led the students to claim that the bar for submissions was too low. With the amount of computer generated text outpacing the ability of people to humans to curate it, there needs some means of distinguishing between the two. Yet automated approaches to determining absolutely whether a text is authentic or not face intrinsic challenges of semantics. Noam Chomsky coined the phrase "Colorless green ideas sleep furiously" giving an example of grammatically correct, but semantically incoherent sentence; some will point out that in certain contexts one could give this sentence (or any phrase) meaning. The first group to use the expression in this regard can be found below from Indiana University. Their work explains in detail an attempt to detect inauthentic texts and identify pernicious problems of inauthentic texts in cyberspace. The site has a means of submitting text that assesses, based on supervised learning, whether a corpus is inauthentic or not. Many users have submitted incorrect types of data and have correspondingly commented on the scores. This application is meant for a specific kind of data; therefore, submitting, say, an email, will not return a meaningful score.
Mountain car problem
Mountain Car, a standard testing domain in Reinforcement learning, is a problem in which an under-powered car must drive up a steep hill. Since gravity is stronger than the car's engine, even at full throttle, the car cannot simply accelerate up the steep slope. The car is situated in a valley and must learn to leverage potential energy by driving up the opposite hill before the car is able to make it to the goal at the top of the rightmost hill. The domain has been used as a test bed in various reinforcement learning papers. == Introduction == The mountain car problem, although fairly simple, is commonly applied because it requires a reinforcement learning agent to learn on two continuous variables: position and velocity. For any given state (position and velocity) of the car, the agent is given the possibility of driving left, driving right, or not using the engine at all. In the standard version of the problem, the agent receives a negative reward at every time step when the goal is not reached; the agent has no information about the goal until an initial success. == History == The mountain car problem appeared first in Andrew Moore's PhD thesis (1990). It was later more strictly defined in Singh and Sutton's reinforcement learning paper with eligibility traces. The problem became more widely studied when Sutton and Barto added it to their book Reinforcement Learning: An Introduction (1998). Throughout the years many versions of the problem have been used, such as those which modify the reward function, termination condition, and the start state. == Techniques used to solve mountain car == Q-learning and similar techniques for mapping discrete states to discrete actions need to be extended to be able to deal with the continuous state space of the problem. Approaches often fall into one of two categories, state space discretization or function approximation. === Discretization === In this approach, two continuous state variables are pushed into discrete states by bucketing each continuous variable into multiple discrete states. This approach works with properly tuned parameters but a disadvantage is information gathered from one state is not used to evaluate another state. Tile coding can be used to improve discretization and involves continuous variables mapping into sets of buckets offset from one another. Each step of training has a wider impact on the value function approximation because when the offset grids are summed, the information is diffused. === Function approximation === Function approximation is another way to solve the mountain car. By choosing a set of basis functions beforehand, or by generating them as the car drives, the agent can approximate the value function at each state. Unlike the step-wise version of the value function created with discretization, function approximation can more cleanly estimate the true smooth function of the mountain car domain. === Eligibility traces === One aspect of the problem involves the delay of actual reward. The agent is not able to learn about the goal until a successful completion. Given a naive approach for each trial the car can only backup the reward of the goal slightly. This is a problem for naive discretization because each discrete state will only be backed up once, taking a larger number of episodes to learn the problem. This problem can be alleviated via the mechanism of eligibility traces, which will automatically backup the reward given to states before, dramatically increasing the speed of learning. Eligibility traces can be viewed as a bridge from temporal difference learning methods to Monte Carlo methods. == Technical details == The mountain car problem has undergone many iterations. This section focuses on the standard well-defined version from Sutton (2008). === State variables === Two-dimensional continuous state space. V e l o c i t y = ( − 0.07 , 0.07 ) {\displaystyle Velocity=(-0.07,0.07)} P o s i t i o n = ( − 1.2 , 0.6 ) {\displaystyle Position=(-1.2,0.6)} === Actions === One-dimensional discrete action space. m o t o r = ( l e f t , n e u t r a l , r i g h t ) {\displaystyle motor=(left,neutral,right)} === Reward === For every time step: r e w a r d = − 1 {\displaystyle reward=-1} === Update function === For every time step: A c t i o n = [ − 1 , 0 , 1 ] {\displaystyle Action=[-1,0,1]} V e l o c i t y = V e l o c i t y + ( A c t i o n ) ∗ 0.001 + cos ( 3 ∗ P o s i t i o n ) ∗ ( − 0.0025 ) {\displaystyle Velocity=Velocity+(Action)0.001+\cos(3Position)(-0.0025)} P o s i t i o n = P o s i t i o n + V e l o c i t y {\displaystyle Position=Position+Velocity} === Starting condition === Optionally, many implementations include randomness in both parameters to show better generalized learning. P o s i t i o n = − 0.5 {\displaystyle Position=-0.5} V e l o c i t y = 0.0 {\displaystyle Velocity=0.0} === Termination condition === End the simulation when: P o s i t i o n ≥ 0.6 {\displaystyle Position\geq 0.6} == Variations == There are many versions of the mountain car which deviate in different ways from the standard model. Variables that vary include but are not limited to changing the constants (gravity and steepness) of the problem so specific tuning for specific policies become irrelevant and altering the reward function to affect the agent's ability to learn in a different manner. An example is changing the reward to be equal to the distance from the goal, or changing the reward to zero everywhere and one at the goal. Additionally, a 3D mountain car can be used, with a 4D continuous state space.
Multi-task learning
Multi-task learning (MTL) is a subfield of machine learning in which multiple learning tasks are solved at the same time, while exploiting commonalities and differences across tasks. This can result in improved learning efficiency and prediction accuracy for the task-specific models, when compared to training the models separately. Inherently, Multi-task learning is a multi-objective optimization problem having trade-offs between different tasks. Early versions of MTL were called "hints". In a widely cited 1997 paper, Rich Caruana gave the following characterization:Multitask Learning is an approach to inductive transfer that improves generalization by using the domain information contained in the training signals of related tasks as an inductive bias. It does this by learning tasks in parallel while using a shared representation; what is learned for each task can help other tasks be learned better. In the classification context, MTL aims to improve the performance of multiple classification tasks by learning them jointly. One example is a spam-filter, which can be treated as distinct but related classification tasks across different users. To make this more concrete, consider that different people have different distributions of features which distinguish spam emails from legitimate ones, for example an English speaker may find that all emails in Russian are spam, not so for Russian speakers. Yet there is a definite commonality in this classification task across users, for example one common feature might be text related to money transfer. Solving each user's spam classification problem jointly via MTL can let the solutions inform each other and improve performance. Further examples of settings for MTL include multiclass classification and multi-label classification. Multi-task learning works because regularization induced by requiring an algorithm to perform well on a related task can be superior to regularization that prevents overfitting by penalizing all complexity uniformly. One situation where MTL may be particularly helpful is if the tasks share significant commonalities and are generally slightly under sampled. However, as discussed below, MTL has also been shown to be beneficial for learning unrelated tasks. == Methods == The key challenge in multi-task learning, is how to combine learning signals from multiple tasks into a single model. This may strongly depend on how well different task agree with each other, or contradict each other. There are several ways to address this challenge: === Task grouping and overlap === Within the MTL paradigm, information can be shared across some or all of the tasks. Depending on the structure of task relatedness, one may want to share information selectively across the tasks. For example, tasks may be grouped or exist in a hierarchy, or be related according to some general metric. Suppose, as developed more formally below, that the parameter vector modeling each task is a linear combination of some underlying basis. Similarity in terms of this basis can indicate the relatedness of the tasks. For example, with sparsity, overlap of nonzero coefficients across tasks indicates commonality. A task grouping then corresponds to those tasks lying in a subspace generated by some subset of basis elements, where tasks in different groups may be disjoint or overlap arbitrarily in terms of their bases. Task relatedness can be imposed a priori or learned from the data. Hierarchical task relatedness can also be exploited implicitly without assuming a priori knowledge or learning relations explicitly. For example, the explicit learning of sample relevance across tasks can be done to guarantee the effectiveness of joint learning across multiple domains. === Exploiting unrelated tasks: Auxiliary learning === In auxiliary learning, one attempts learning a group of principal tasks using a group of auxiliary tasks, unrelated to the principal ones. With the right unrelated tasks, joint learning of unrelated tasks which use the same input data have been shown to be beneficial, and provide significant improvement over standard MTL. The reason is that prior knowledge about task relatedness can lead to sparser and more informative representations for each task grouping, essentially by screening out idiosyncrasies of the data distribution. It has been proposed to build on a prior multitask methodology by favoring a shared low-dimensional representation within each task grouping, and imposing a penalty on tasks from different groups which encourages the two representations to be orthogonal. Learning with auxiliary unrelated tasks poses two major challenges: Finding useful auxiliary tasks and combining losses of all tasks in a useful way. Some methods can learn these from data together with the training process, and combine tasks efficiently. === Transfer of knowledge === Related to multi-task learning is the concept of knowledge transfer. Whereas traditional multi-task learning implies that a shared representation is developed concurrently across tasks, transfer of knowledge implies a sequentially shared representation. Large scale machine learning projects such as the deep convolutional neural network GoogLeNet, an image-based object classifier, can develop robust representations which may be useful to further algorithms learning related tasks. For example, the pre-trained model can be used as a feature extractor to perform pre-processing for another learning algorithm. Or the pre-trained model can be used to initialize a model with similar architecture which is then fine-tuned to learn a different classification task. === Multiple non-stationary tasks === Traditionally Multi-task learning and transfer of knowledge are applied to stationary learning settings. Their extension to non-stationary environments is termed Group online adaptive learning (GOAL). Sharing information could be particularly useful if learners operate in continuously changing environments, because a learner could benefit from previous experience of another learner to quickly adapt to their new environment. Such group-adaptive learning has numerous applications, from predicting financial time-series, through content recommendation systems, to visual understanding for adaptive autonomous agents. === Multi-task optimization === Multi-task optimization focuses on solving optimizing the whole process. The paradigm has been inspired by the well-established concepts of transfer learning and multi-task learning in predictive analytics. The key motivation behind multi-task optimization is that if optimization tasks are related to each other in terms of their optimal solutions or the general characteristics of their function landscapes, the search progress can be transferred to substantially accelerate the search on the other. The success of the paradigm is not necessarily limited to one-way knowledge transfers from simpler to more complex tasks. In practice an attempt is to intentionally solve a more difficult task that may unintentionally solve several smaller problems. There is a direct relationship between multitask optimization and multi-objective optimization. In some cases, the simultaneous training of seemingly related tasks may hinder performance compared to single-task models. Commonly, MTL models employ task-specific modules on top of a joint feature representation obtained using a shared module. Since this joint representation must capture useful features across all tasks, MTL may hinder individual task performance if the different tasks seek conflicting representation, i.e., the gradients of different tasks point to opposing directions or differ significantly in magnitude. This phenomenon is commonly referred to as negative transfer. To mitigate this issue, various MTL optimization methods have been proposed. It has been reported that meta-knowledge transfer could help avoid negative transfer.Besides, the per-task gradients are combined into a joint update direction through various aggregation algorithms or heuristics. There are several common approaches for multi-task optimization: Bayesian optimization, evolutionary computation, and approaches based on Game theory. ==== Multi-task Bayesian optimization ==== Multi-task Bayesian optimization is a modern model-based approach that leverages the concept of knowledge transfer to speed up the automatic hyperparameter optimization process of machine learning algorithms. The method builds a multi-task Gaussian process model on the data originating from different searches progressing in tandem. The captured inter-task dependencies are thereafter utilized to better inform the subsequent sampling of candidate solutions in respective search spaces. ==== Evolutionary multi-tasking ==== Evolutionary multi-tasking has been explored as a means of exploiting the implicit parallelism of population-based search algorithms to simultaneously progress multiple distinct optimization tasks. By mapping all task
Alexander Y. Tetelbaum
Alexander Y. Tetelbaum (born August 16, 1948) is a Ukrainian American computer scientist, inventor, and academic who has contributed to electronic design automation (EDA) and artificial intelligence (AI) since the late 1960s; and holds 46 U.S. patents in EDA and related fields. Tetelbaum is the founding president of International Solomon University, the first Jewish university in Ukraine, established during a period of renewed efforts to address antisemitism in Ukraine. == Early life and education == He graduated from a Kyiv mathematical high school with a silver medal in 1966. Tetelbaum enrolled at the Kyiv Polytechnic Institute (KPI), now National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" in 1966, graduating in 1972 with an MS in Electronics with honors. He earned his PhD in Electrical and Computer Engineering from KPI in 1975, with a dissertation on electronic design automation, and his Doctor of Engineering Science in 1986. == Academic career == Tetelbaum began his academic career at KPI in 1973 as a junior scientist, becoming a professor in the Computer and Electrical Engineering Department in 1980. Later, he founded and served as president of International Solomon University in Kyiv from 1991 to 1996, the first Jewish university in Ukraine. The university became a major academic center for computer science and Jewish studies in the post-Soviet era. He was a visiting and adjunct professor at Michigan State University from 1993 to 1996. == Professional career == Tetelbaum worked as an engineer at the Kiev Institute of Cybernetics from 1972 to 1973, and later, he led the Design Automation Lab at Kyiv Polytechnic Institute from 1975 to 1987. In the United States, he served as EDA manager at Silicon Graphics Corporation from 1996 to 1998 and principal engineer at LSI Corporation from 1998 to 2012. He founded and served as CEO of Abelite Design Automation, Inc., from 2012 to 2022. == Contributions in computer science == Tetelbaum has contributed to electronic design automation (EDA) and artificial intelligence (AI) since the 1960s. His early work included methods for EDA, particularly physical design automation and mathematical optimization; and he developed force-directed placement and topological routing methods. Tetelbaum generalized Rent's rule for hierarchical systems and large blocks, proposing a graph-based framework that extends applicability to arbitrary partition sizes with improved accuracy. Additional IEEE and related conference contributions from the mid-1990s include: "Path Search for Complicated Function", 1995 IEEE International Symposium on Circuits and Systems "A Performance-driven Placement Approach of Standard Cells" (International Conference on Intelligent Systems, 1995) "Framework of a New Methodology for Behavioral to Physical Design Linkage" (38th Midwest Symposium on Circuits and Systems, 1996) Statistical timing design and variations Test Methodologies These and other works and patents contributed to timing-driven placement, crosstalk reduction, clock tree synthesis, and interconnect optimization in VLSI design. == Patents == Tetelbaum holds 46 U.S. patents in EDA and related fields. Notable examples include: For the full list of patents, see Justia Patents or Google Patents. == Publications == === Early publications in the Soviet Union === Before the appearance of American books on electronic design automation (EDA), Tetelbaum published several scientific books and monographs on the subject in Russian/Ukrainian. Electronic Design Automation, Kiev: Znanie Publisher, 1975. Planar Design of Electronic Circuits, Kiev: Znanie Publisher, 1977. Formal Design of Computer Systems, Moscow: Sovetskoe Radio, 1979. CAD of Electronic Equipment: Topological Approach, Kiev: Vyssha Shkola, 1980; 2nd ed. 1981. Automated Design of Electronic Circuits (1981) CAD of VLSI Circuits, Kiev: Vyssha Shkola, 1983. Topological Algorithms of Multilayer Printed Circuit Boards Routing, Moscow: Radio i Svyaz, 1983. CAD of VLSI Circuits on Master Slice Chips, Moscow: Radio i Svyaz, 1988. Increasing the Effectiveness of CAD Systems, Kiev: UMKVO, 1991. === Scientific Monographs (English) === Minimum Number of Timing Signoff Corners (2022) Interviewing AI (2026) The AI Debate (2026) New Nostradamus Predictions: 2026: The Next Decade & Beyond (2035–2050+) (2026) For a consolidated record of Tetelbaum's publications, see Alexander Y. Tetelbaum, Wikidata Q4720205. === Other publications === Tetelbaum also published educational books on problem-solving methods: Yes-No Puzzles-Games Puzzle Games for Kids Solving Non-Standard Problems Solving Non-Standard Very Hard Problems Additionally, Tetelbaum published three thrillers: Omerta Operations Executive Director Eruption Yacht Finally, he published his memoir and an entertaining book: Unfinished Equations Artificially Intelligent Humor
Problem solving
Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to get from point A to B) to complex issues in business and technical fields. The former is an example of simple problem solving (SPS) addressing one issue, whereas the latter is complex problem solving (CPS) with multiple interrelated obstacles. Another classification of problem-solving tasks is into well-defined problems with specific obstacles and goals, and ill-defined problems in which the current situation is troublesome but it is not clear what kind of resolution to aim for. Similarly, one may distinguish formal or fact-based problems requiring psychometric intelligence, versus socio-emotional problems which depend on the changeable emotions of individuals or groups, such as tactful behavior, fashion, or gift choices. Solutions require sufficient resources and knowledge to attain the goal. Professionals such as lawyers, doctors, programmers, and consultants are largely problem solvers for issues that require technical skills and knowledge beyond general competence. Many businesses have found profitable markets by recognizing a problem and creating a solution: the more widespread and inconvenient the problem, the greater the opportunity to develop a scalable solution. There are many specialized problem-solving techniques and methods in fields such as science, engineering, business, medicine, mathematics, computer science, philosophy, and social organization. The mental techniques to identify, analyze, and solve problems are studied in psychology and cognitive sciences. Also widely researched are the mental obstacles that prevent people from finding solutions; problem-solving impediments include confirmation bias, mental set, and functional fixedness. == Definition == The term problem solving has a slightly different meaning depending on the discipline. For instance, it is a mental process in psychology and a computerized process in computer science. There are two different types of problems: ill-defined and well-defined; different approaches are used for each. Well-defined problems have specific end goals and clearly expected solutions, while ill-defined problems do not. Well-defined problems allow for more initial planning than ill-defined problems. Solving problems sometimes involves dealing with pragmatics (the way that context contributes to meaning) and semantics (the interpretation of the problem). The ability to understand what the end goal of the problem is, and what rules could be applied, represents the key to solving the problem. Sometimes a problem requires abstract thinking or coming up with a creative solution. Problem solving has two major domains: mathematical problem solving and personal problem solving. Each concerns some difficulty or barrier that is encountered. === Psychology === Problem solving in psychology refers to the process of finding solutions to problems encountered in life. Solutions to these problems are usually situation- or context-specific. The process starts with problem finding and problem shaping, in which the problem is discovered and simplified. The next step is to generate possible solutions and evaluate them. Finally a solution is selected to be implemented and verified. Problems have an end goal to be reached; how you get there depends upon problem orientation (problem-solving coping style and skills) and systematic analysis. Mental health professionals study the human problem-solving processes using methods such as introspection, behaviorism, simulation, computer modeling, and experiment. Social psychologists look into the person-environment relationship aspect of the problem and independent and interdependent problem-solving methods. Problem solving has been defined as a higher-order cognitive process and intellectual function that requires the modulation and control of more routine or fundamental skills. Empirical research shows many different strategies and factors influence everyday problem solving. Rehabilitation psychologists studying people with frontal lobe injuries have found that deficits in emotional control and reasoning can be re-mediated with effective rehabilitation and could improve the capacity of injured persons to resolve everyday problems. Interpersonal everyday problem solving is dependent upon personal motivational and contextual components. One such component is the emotional valence of "real-world" problems, which can either impede or aid problem-solving performance. Researchers have focused on the role of emotions in problem solving, demonstrating that poor emotional control can disrupt focus on the target task, impede problem resolution, and lead to negative outcomes such as fatigue, depression, and inertia. In conceptualization,human problem solving consists of two related processes: problem orientation, and the motivational/attitudinal/affective approach to problematic situations and problem-solving skills. People's strategies cohere with their goals and stem from the process of comparing oneself with others. === Cognitive sciences === Among the first experimental psychologists to study problem solving were the Gestaltists in Germany, such as Karl Duncker in The Psychology of Productive Thinking (1935). Perhaps best known is the work of Allen Newell and Herbert A. Simon. Experiments in the 1960s and early 1970s asked participants to solve relatively simple, well-defined, but not previously seen laboratory tasks. These simple problems, such as the Tower of Hanoi, admitted optimal solutions that could be found quickly, allowing researchers to observe the full problem-solving process. Researchers assumed that these model problems would elicit the characteristic cognitive processes by which more complex "real world" problems are solved. An outstanding problem-solving technique found by this research is the principle of decomposition. === Computer science === Much of computer science and artificial intelligence involves designing automated systems to solve a specified type of problem: to accept input data and calculate a correct or adequate response, reasonably quickly. Algorithms are recipes or instructions that direct such systems, written into computer programs. Steps for designing such systems include problem determination, heuristics, root cause analysis, de-duplication, analysis, diagnosis, and repair. Analytic techniques include linear and nonlinear programming, queuing systems, and simulation. A large, perennial obstacle is to find and fix errors in computer programs: debugging. === Logic === Formal logic concerns issues like validity, truth, inference, argumentation, and proof. In a problem-solving context, it can be used to formally represent a problem as a theorem to be proved, and to represent the knowledge needed to solve the problem as the premises to be used in a proof that the problem has a solution. The use of computers to prove mathematical theorems using formal logic emerged as the field of automated theorem proving in the 1950s. It included the use of heuristic methods designed to simulate human problem solving, as in the Logic Theory Machine, developed by Allen Newell, Herbert A. Simon and J. C. Shaw, as well as algorithmic methods such as the resolution principle developed by John Alan Robinson. In addition to its use for finding proofs of mathematical theorems, automated theorem-proving has also been used for program verification in computer science. In 1958, John McCarthy proposed the advice taker, to represent information in formal logic and to derive answers to questions using automated theorem-proving. An important step in this direction was made by Cordell Green in 1969, who used a resolution theorem prover for question-answering and for such other applications in artificial intelligence as robot planning. The resolution theorem-prover used by Cordell Green bore little resemblance to human problem solving methods. In response to criticism of that approach from researchers at MIT, Robert Kowalski developed logic programming and SLD resolution, which solves problems by problem decomposition. He has advocated logic for both computer and human problem solving and computational logic to improve human thinking. === Engineering === When products or processes fail, problem solving techniques can be used to develop corrective actions that can be taken to prevent further failures. Such techniques can also be applied to a product or process prior to an actual failure event—to predict, analyze, and mitigate a potential problem in advance. Techniques such as failure mode and effects analysis can proactively reduce the likelihood of problems. In either the reactive or the proactive case, it is necessary to build a causal explanation through a process of diagnosis. In deriving an explanation of effects in terms of causes, abduction generates new ideas or hypothes